An MRI apparatus uses a magnet of mainly a superconducting magnet. In some cases, however, it uses a permanent magnet and a normal conducting magnet. The magnet used in the MRI apparatus generates a static magnetic field requiring an accuracy which has a variation of about one millionth of a magnetic field intensity come to a problem.
The magnetic fields used in the MRI apparatus are broadly classified into the following three types.
(1) A magnetic field that is temporally and spatially constant and that normally has an intensity of 0.1 to several teslas or more, having the amount of variation within a space for performing imaging (space of a sphere or ellipsoid having diameter of 30 to 40 cm) of several ppm.
(2) A spatially gradient magnetic field and changes with a time constant of one second or less.
(3) A magnetic field generated by a high-frequency electromagnetic wave with a frequency (several MHz or more) that corresponds to nuclear magnetic resonance.
Among the three, the magnetic field (1) is required to be temporally constant and to have a highly accurate homogeneity spatially, in a space of area in which tomographic imaging is performed on a human body. Being highly accurate means having an accuracy with an order of one millionth, for example, ±1.5 ppm in an imaging space field of view (FOV) having a diameter of, for example, 40 cm. A magnetic field distribution which requires extremely highly accurate homogeneity is achieved by executing accurate adjustment of the magnetic field distribution after production and excitation of a magnet. A typical error magnetic field caused by a manufacturing error is 1000 times or more than a permissible error margin of the magnetic field demanded for a homogeneous magnetic field. This means that it is necessary to reduce an error magnetic field from several hundred ppm to several ppm in magnetic field adjustment (referred to as shimming) performed at a time of installation of a magnet after manufacturing of the magnet. Accordingly, the shimming requires an extremely high-level magnetic field adjustment technique.
Conventionally, this type of shimming uses a magnetic piece including an iron piece that is passively magnetized, a permanent magnet piece, a current loop, or the like, namely, something that has a magnetic moment (hereinafter, for simplification, referred to as a magnetic moment). In shimming, this magnetic moment is placed around a magnetic-field applied area. Adjusting an intensity and a placement position of the magnetic moment achieves a magnetic field distribution required for the magnetic-field applied area. In an MRI apparatus, the magnetic-field applied area means the imaging space FOV for diagnosis. Shimming is performed to achieve a magnetic field distribution with homogeneity within the space.
A typical magnetic moment for shimming is placed so as to cancel an error magnetic field distribution Ber. The error magnetic field distribution Ber is a vector having the amount of difference between a measurement magnetic field at each of magnetic field measurement positions and a target magnetic field distribution as an element. Herein, there are several hundreds of magnetic field measurement positions and there are several hundreds to tens of thousands or more of magnetic moment placement positions. With this placement, calculating placement of the magnetic moment for shimming would be a large-scale calculation.
Patent Literature 1, for example, describes as a calculation method for placing the magnetic moment, a truncated singular value decomposition (hereinafter, referred to as TSVD) method.
According to the TSVD method, a magnetic field distribution Bcom generated in a measured magnetic field area by a magnetic moment M placed for shimming is considered to be expressed as:Bcom=A·M  (1)
Based on the above, the magnetic moment M to be placed for shimming is determined such that the magnetic field distribution Bcom substantially corresponds to the error magnetic field distribution Ber.
Hereinafter in this description, the magnetic moment to be placed for shimming will be referred to simply as a shimming magnetic moment.
The shimming magnetic moment M is a vector having a magnetic moment magnitude at each of placement positions as an element. The number of elements may be several hundreds, several thousands or more. The magnetic field distribution Bcom is a vector having, as an element, the magnetic field intensity generated at each of magnetic field measurement points by the shimming magnetic moment M. A response matrix A is a matrix representing a relationship between the magnitude of the magnetic moment placed at each of the positions as the shimming magnetic moment M and the magnetic field intensity at each of the magnetic field measurement points. The response matrix A has an element of (number of magnetic field measurement points)×(number of magnetic moment placement positions).
Moreover, according to Patent Literature 1, to obtain the shimming magnetic moment M that satisfies:Ber≈A·M  (2)the following formula,M=−A*·Ber  (3)
is used to obtain a general inverse matrix A* using the truncated singular value decomposition (hereinafter, TSVD) method. Accordingly, the shimming magnetic moment M is obtained as,M=Σ(−vj·Cj/λj)  (4)
Calculation of sum (Σ) in Formula (4) is performed based on an eigenmode obtained by singular value decomposition (SVD). The eigenmode represents a relationship between a base vj of the shimming magnetic moment M and a base uj of the magnetic field distribution Bcom. Each of the eigenmodes has a singular value λj that represents a magnetic field intensity of a unit magnetic moment (norm: 1) per placement. In addition, eigenmode intensity Cj has a same unit as the magnetic field intensity and is determined by an inner product of eigen magnetic field distribution and the error magnetic field distribution Ber.
In addition (calculation of Σ) of Formula (4), as a reference value for selecting the eigenmode to be a target of the addition, the eigenmode intensity and an order of the eigenmode are used. The order of the eigenmode represents the number indicating the order when the singular value λj of each of the eigenmodes is arranged in order from the highest value.
In other words, as an eigenmode used in addition (calculation of Σ) in Formula (4), selection is performed such that the eigenmode intensity Cj is sufficiently smaller than the final permissible error magnetic field, and the order of the eigenmode is a predetermined upper limit or less. At this time, a shimming operator has determined the upper limit value of the order of the eigenmode used in addition (calculation of Σ) in Formula (4), namely, the eigenmode as a calculation target of the shimming magnetic moment M (hereinafter, referred to as the upper limit value of the order at the time of addition of the eigenmode) has been determined by appropriately comparing the eigenmode intensity Cj with the permissible intensity of the magnetic field error.
FIGS. 6A and 6B are exemplary graphs, described in Patent Literature 1, displayed on a display device at a time of selecting the eigenmode used in addition of obtaining placement of the shimming magnetic moment. FIG. 6A is a graph before shimming and FIG. 6B is a graph after shimming. The vertical axis of the graph represents logarithm of the eigenmode intensity, and the horizontal axis represents the order of the eigenmode. In the graph, the x-mark 16 in the graph represents one eigenmode, and the circled x-mark 15 represents the eigenmode used for addition in Formula (4). The horizontal line 3 in the graph is a line representing a lower limit value of the eigenmode intensity Cj used in addition. The eigenmodes positioned above this line are candidates for addition. The vertical line 2 represents an upper limit value of the order at the time of addition of the eigenmodes used for the addition (namely, the lower limit value of the singular value λj).
Accordingly, calculation using Formula (4) is performed for the eigenmodes (eigenmodes represented by the circled x-marks 15) determined by the horizontal line 3 (lower limit value of the eigenmode intensity Cj) and by the vertical line 2 (lower limit value of the singular value λj). With this calculation, the shimming magnetic moment M is obtained. Subsequently, by using Formula (1), it is possible to calculate the magnetic field distribution Bcom to be corrected by the shimming magnetic moment M.
Conventionally, a residual magnetic field distribution Bres that remains after correction has been estimated by the formula,Bres=Ber−Bcom  (5)
and based on the magnitude of the amount of variation of the residual magnetic field distribution Bres, validity of the eigenmode determined by the two lines of the horizontal line 3 and the vertical line 2, namely validity of the condition for addition in Formula (4) has been confirmed.
In FIG. 6A, as an index that indicates the magnitude of the amount of variation of the residual magnetic field distribution Bres, a value has been obtained by dividing a difference between the maximum value and the minimum value (hereinafter, referred to as a peak to peak (PP) value) of the element of the residual magnetic field distribution Bres, by an average magnetic field intensity, a target magnetic field intensity, or the like, in a measured magnetic field area. A ppm value (one millionth value) of the obtained value is indicated at an upper portion of the graph as an attainable homogeneity 17.
A shimming operator compares the displayed attainable homogeneity 17 with the predetermined target accuracy. When the attainable homogeneity 17 is larger than the target accuracy, the operator increases the upper limit value of the order at the time of addition of the eigenmode so as to increase the eigenmode to be used in addition in Formula (4). With this operation, the shimming magnetic moment M is readjusted to improve the attainable homogeneity 17.
This type of shimming method can be defined as operation for setting a suitable target magnetic field intensity, the vertical line 2, the horizontal line 3, or the like, by using the graphs in FIGS. 6A and 6B. In this context, the shimming operation might be slightly in a form of trial and error operation. Still, repeating this adjustment operation, it is possible to perform adjustment (shimming) to reliably achieve a good magnetic field distribution as illustrated in FIG. 6B. Note that the attainable homogeneity 17 illustrated in FIG. 6A is an estimation value before shimming, and the attainable homogeneity 17a illustrated in FIG. 6B is a value obtained from the measured magnetic field after shimming.